US6608717B1 - Optical coherence microscope and methods of use for rapid in vivo three-dimensional visualization of biological function - Google Patents

Optical coherence microscope and methods of use for rapid in vivo three-dimensional visualization of biological function Download PDF

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US6608717B1
US6608717B1 US09/493,896 US49389600A US6608717B1 US 6608717 B1 US6608717 B1 US 6608717B1 US 49389600 A US49389600 A US 49389600A US 6608717 B1 US6608717 B1 US 6608717B1
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sample
light
path
biological sample
ocm
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June I. Medford
Richard C. Haskell
Barbara M. Hoeling
Daniel C. Petersen
Ruye Wang
Mary E. Williams
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Colorado State University Research Foundation
Harvey Mudd College
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B9/00—Measuring instruments characterised by the use of optical techniques
    • G01B9/04—Measuring microscopes
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00—Measuring for diagnostic purposes; Identification of persons
    • A61B5/0059—Measuring for diagnostic purposes; Identification of persons using light, e.g. diagnosis by transillumination, diascopy, fluorescence
    • A61B5/0062—Arrangements for scanning
    • A61B5/0066—Optical coherence imaging
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00—Measuring for diagnostic purposes; Identification of persons
    • A61B5/0059—Measuring for diagnostic purposes; Identification of persons using light, e.g. diagnosis by transillumination, diascopy, fluorescence
    • A61B5/0073—Measuring for diagnostic purposes; Identification of persons using light, e.g. diagnosis by transillumination, diascopy, fluorescence by tomography, i.e. reconstruction of 3D images from 2D projections
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/47—Scattering, i.e. diffuse reflection
    • G01N21/4795—Scattering, i.e. diffuse reflection spatially resolved investigating of object in scattering medium
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B21/00—Microscopes
    • G02B21/0004—Microscopes specially adapted for specific applications
    • G02B21/002—Scanning microscopes
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
    • G02B6/24—Coupling light guides
    • G02B6/26—Optical coupling means
    • G02B6/28—Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals
    • G02B6/293—Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals with wavelength selective means
    • G02B6/29346—Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals with wavelength selective means operating by wave or beam interference
    • G02B6/29349—Michelson or Michelson/Gires-Tournois configuration, i.e. based on splitting and interferometrically combining relatively delayed signals at a single beamsplitter

Definitions

  • the present invention relates to an optical coherence microscope (OCM) for study of problems in developmental biology and biotechnology. More particularly, the invention is used for imaging cells located up to four millimeters or more below the surface of living tissue.
  • OCM optical coherence microscope
  • OCM optical coherence microscopy
  • the image formation rate of the confocal microscope is sufficiently fast to follow the dynamic behaviors of cells as they migrate or of retinal cell axons as they extend, actively sense, and retract projections toward cells in the tectum (O'Rourke et al., 1994).
  • light scattering in embryonic tissue reduces the signal-to-noise ratio of a confocal microscope, limiting the depth of the specimen that can be explored to about 200 ⁇ m (Schmitt et al., 1994b).
  • a second imaging technology is magnetic resonance imaging (MRI), recently extended to the microscopic domain so that it can now resolve a 12 ⁇ m cube in living embryos (Jacobs and Fraser, 1994).
  • MRI magnetic resonance imaging
  • GFP green fluorescence protein
  • An optical coherence microscope uses the principles of confocal microscopy, with an additional coherence gate that excludes back-scattered light from out-of-focus planes, resulting in a signal-to-noise ratio that is enhanced by 6 orders of magnitude (lzatt et al., 1994a,b). A resolution of 10 ⁇ m has been achieved in both the lateral and depth directions (Huang et al., 1991b). Optical fiber and solid state sources/detectors are typically used, so the instrument is inherently rugged. OCM overcomes the depth limitation of confocal microscopy and is currently faster than MRI. And at an estimated cost of under $10,000 the instrument is two orders of magnitude less expensive than the MRI microscope.
  • the coherence gate in OCM is achieved by superposing a Michelson interferometer on the confocal microscope.
  • Back-scattered light from the specimen interferes coherently with light returning from an added reference arm only when the two optical paths are equal.
  • the amplitude of interference fringes becomes the signal; this signal is appreciable only for light back-scattered from a narrow range of depths in the specimen.
  • a lateral image optical section
  • the spot size of the focused beam determines the lateral resolution.
  • the interferometer output is monitored for interference fringes that occur when light is reflected or back-scattered from a point a distance along the tested fiber equal to the reference path length.
  • the spatial resolution along the tested fiber is one-half the coherence length because the fiber is traversed twice in that leg of the interferometer. (Actually the geometrical spatial resolution is even smaller by a factor of n, where n is the refractive index of the fiber.) For a spectral width of 30 nm, the geometrical spatial resolution along a fiber is 7 ⁇ m.
  • Interference occurs at the output of the OCM only between the same polarization components of the electric fields returning from the reference mirror and the sample, respectively.
  • Birefringence effects in the optical fibers or in the sample may alter the relative magnitude and phase of the two polarization components emitted by the source and hence reduce the amplitude of the interference fringes at the photodetector.
  • some workers have used polarization-preserving fibers and linearly polarized light to eliminate polarization-dispersion effects that lead to different optical path lengths for different polarization states (Clivaz et al., 1992). Kobayashi et al.
  • the present invention provides a high resolution optical coherence microscope system for visualizing structures below a surface of a biological sample.
  • the system includes a light source emitting light in a wavelength of between 700 and 1500 nm, the light being directed along a sample path and a reference path.
  • the length of at least one of the paths is a modulated path having a selected amplitude of modulation that is equal to or less than about 3 fringes of the wavelength.
  • the modulation may occur at a frequency of at least about 50 kHz, 100 kHz, 300 kHz or at a higher frequency.
  • the light directed along the sample path may scan the biological sample, the scan resulting in an image of a portion of the biological sample; the portion may be between about 100 ⁇ m and about 4000 ⁇ m below the surface of the sample.
  • the image may include one or more layers. Each layer may be derived from multiple voxels all corresponding to substantially the same depth below the surface of the sample.
  • the image may include at least about 50 distinct layers, each of the layers derived from a distinct group of voxels, with all voxels for each distinct layer corresponding to substantially the same distinct depth below the surface of the sample.
  • the image likewise may include blended voxels of several layers, such that the image may be a three-dimensional rendering of the portion of the biological sample.
  • the OCM system of the invention further may include a coherence volume about a plane at which the length of the sample is equal to the length of the reference path, such that the coherence volume exists below the surface of the biological sample.
  • the light from the sample path may enter the sample and taper to a beam waist diameter of not more than 20 ⁇ m within the sample.
  • the beam waist is coincident with the coherence volume, such that resolution of structures within the sample is a distance less than or equal to the diameter of the beam waist.
  • the invention further provides a method of visualizing a structure beneath a surface of a biological sample, employing the OCM system described herein.
  • the OCM system also allows a method of analyzing a biological function based on visualization of in vivo changes in structures beneath a surface of a biological sample.
  • the function to be analyzed may include, for example, gene regulation, development, messenger response, and stress.
  • the invention also provides a method of visualizing a structure beneath a surface of a biological sample.
  • the method may include the steps of: providing light having a wavelength between 700 and 1500 nm; dividing the light into a sample light path and a reference light path; modulating the length of at least one of the light paths at an amplitude no greater than about 3 fringes of the wavelength; directing light from the sample path into the biological sample, such that the light tapers to a beam waist at a selected depth below the surface of the sample, and such that the beam waist is coincident with a coherence volume about a plane of equal path length of the sample path and the reference path; and detecting an image at the selected depth below the surface of the sample to visualize the structure.
  • the directing step may be repeated at least 100 times, and after each directing step, the method may include the additional step of translocating the sample light path to a different position in the biological sample.
  • the image thus visualized may indicate a difference between a mutant biological sample and a non-mutant biological sample.
  • the image may include a pattern of light scatter, wherein the pattern correlates with a characteristic of the biological sample, such as, for example, gene activity, differentiation, cell elongation, cell dormancy, stress response, and pathogen response.
  • FIG. 1 presents the optical schematic of a fiber-optic optical coherence microscope (OCM).
  • FIG. 2 is an image of a Ronchi ruling visualized through 1.2 mm of a highly scattering solution of polystyrene latex spheres.
  • FIG. 3 is a typical plots of OCM fringe amplitude versus depth, averaged over horizontal slices in a plant preparation.
  • FIG. 4 is a typical plots of OCM fringe amplitude versus depth, averaged over horizontal slices in a frog preparation.
  • FIG. 5 illustrates that relationship between noise in the reference beam versus reference beam power.
  • FIG. 6 shows the impedance of mounted and unmounted piezos as a function of the driving voltage frequency.
  • FIG. 7 shows the displacement of the piezo per volt applied at each of the resonance frequencies.
  • FIG. 8 illustrates the phase dependence of the output fringe signal.
  • FIG. 9 shows the experimental values for the powers of the interferometer output signal in the first two harmonics as a function of the piezo driving voltage.
  • FIG. 10 is an optical schematic of a modified OCM.
  • the present invention discloses an optical coherence microscope capable of addressing fundamental problems in developmental biology. Results for two exemplary developmental systems, the frog Xenopus laevis and the plant Arabidopsis thaliana , are presented herein.
  • the invention is likewise suitable for application to numerous other taxa including, for example, Drosophila, zebrafish, and virtually any agriculturally or scientifically important plant.
  • the present invention is also broadly applicable to other biological systems wherein the events, structures, cells, and/or processes to be visualized are not accessible to light microscopy.
  • the invention is particularly suitable for developmental biology studies of structures and events within 4 mm, preferably within 3 mm, more preferably within 2 mm, and most preferably within 1 mm, of a tissue surface.
  • the invention contemplates use of the disclosed OCM for other purposes, such as, for example, diagnostics and functional genomic analysis.
  • data for a three-dimensional image formed by stacking successive lateral images from different depths can be acquired in less than a minute.
  • the present invention is particularly well suited for high throughput functional genomic analysis, each OCM having the capability of tracking development and other gene-regulated events in many plants per day. In this aspect of the invention, 25, 50, 100, 250, 500, or more plants may be screened per day, depending on the nature of the screening.
  • the resolution of the OCM makes it ideally suited for following development within amphibian embryos, where single cell size is typically greater than 10 ⁇ m and critical developmental events take place within the first few hundred micrometers. More conventional microscopy (confocal microscopy, video microscopy) is not suitable for following much of the embryonic development because of the highly scattering nature of the frog embryo cytoplasm and the optical aberrations inherent in confocal imaging deep into tissues (Schmitt et al., 1994b). Recently, using an MRI microscope, Jacobs and Fraser (1994) were able to follow events within the interior of a frog embryo during gastrulation and neurulation.
  • the plant body is predominantly formed post-embryonically through the activity of specialized tissues called meristems (Steeves and Wales, 1989).
  • Current understanding of the molecular mechanisms governing the function and formation of meristems is very limited.
  • advances in the understanding of meristem formation have been made through the genetic analysis of the small crucifer Arabidopsis thaliana (Mayer et al., 1991; Barton and Poethig, 1993).
  • Arabidopsis two meristems the primary root and shoot apical meristems, are formed embryonically, while the secondary (lateral) root and shoot meristems appear post-embryonically.
  • the shoot apical meristem of Arabidopsis lies below the surface, and an embryo of Arabidopsis lies within a layer of pigmented cells.
  • an embryo of Arabidopsis lies within a layer of pigmented cells.
  • the shoot apical meristem forms the vast portion of tissues and organs in a plant (e.g. leaves). Leaves are directly initiated on the flanks of the shoot apical meristem through an asymmetrical expansion of the meristem, leading to a bulge, which after further unidirectional expansion becomes clearly delimited as a leaf primordium (Steeves and Wales, 1989). Surgical experiments have demonstrated that previously initiated leaf primordia have an inhibitory effect on the positioning of the subsequent primordium, causing it to form on the point farthest from the two previously initiated leaves (Snow and Snow, 1962).
  • OCM permits detection of organ initiation, dorsoventrality, and other processes deeply buried in 1 to 2 millimeters of tissue at a resolution of at least 10 ⁇ m. These dimensions fall within the optimal ranges of OCM and are not suited for analysis by other techniques.
  • OCM permits observation of altered patterns of phyllotaxy arising from genetic mutations or exogenous application of hormones.
  • a high amount of backscattered light detected in cells and tissues by OCM correlates strongly with cells and tissues known to be active in transcription and differentiation.
  • OCM provides a tool to follow any active process, natural or induced in vivo.
  • the present invention thus expressly contemplates uses of OCM embodiments of the invention in various approaches to following active biological processes including, for example, functional genomic analysis, developmental studies, tracking responses to biological signals such as hormones and pathogen elicitors; and the like.
  • the microscope of the invention is capable of imaging cells located below the surface of living tissue, even though light scattering in the specimen would render it opaque to a conventional or confocal light microscope.
  • Depth penetration is achieved by use of a near infrared superluminescent diode light source with a coherence length of 20 ⁇ m together with a coherence gate based on a Michelson interferometer. This combination excludes light back-scattered from out-of-focus planes, giving a depth resolution of 10 ⁇ m.
  • Lateral resolution of 10 ⁇ m or better is achieved by focusing the illuminating beam down to a small spot.
  • Two-dimensional lateral scanning of the beam spot produces an optical section at a fixed depth in the sample.
  • a three-dimensional image is obtained by stacking successive optical sections at different depths. Such three-dimensional scans typically take less than a minute.
  • FIG. 1 presents the optical schematic of a fiber-optic OCM.
  • the superluminescent diode (SLD) is a laser diode with end facets that have been anti-reflection coated so that no lasing occurs, and hence the full spectral breadth of the transition appears in the output.
  • the center wavelength lies in the near infrared (e.g., 850 nm) where the absorption coefficient of biological tissue is near its minimum.
  • a 30 nm fill-width-at-half-maximum (FWHM) spectral width of the SLD yields a final depth resolution (FWHM of the Gaussian visibility function) of 11 ⁇ m/n , where the refractive index, n, of tissue is close to 1.40 (Bolin et al., 1989).
  • the helium-neon laser beam (633 nm) serves simply to visualize the focused spot, and both beams are coupled into single-mode optical fibers. The two fibers are combined in a fused region called a “2 ⁇ 1 coupler”.
  • Each source beam is split and sent along the two paths of the Michelson interferometer by the 2 ⁇ 2 coupler, a similar fused region of two fibers that mixes their spatial modes.
  • the sample path fiber is terminated with an aspheric collimating lens, and the beam is then focused by a doublet lens to a spot diameter of 9 ⁇ m.
  • the sample fiber/focusing lens assembly is mounted on a 3-D scanning stage consisting of a 1-D translation stage powered by a DC motor and a pair of galvo-scanners in an x-y mount.
  • the closed-loop galvo-scanners raster-scan the horizontal plane while the closed-loop DC motor steps along the depth dimension, so the waist of the focused beam explores a sample volume and an OCM image is formed.
  • the reference path fiber is also terminated with an aspheric collimating lens and is led to a reference mirror (retroreflector) that is mounted on another translation stage driven by a closed-loop DC motor.
  • a reference mirror retroreflector
  • the reference mirror is translated to keep the beam waist coincident with the coherence volume (position of equal path lengths in the interferometer). This last point is important because the Rayleigh range of the focused beam is roughly 60 ⁇ m, so the beam rapidly expands and the lateral resolution quickly degrades as the coherence volume deviates from the beam waist.
  • the instrument may also include matching piezoelectric cylinders around which are wrapped the reference path fiber and the sample path fiber.
  • the circumference of each cylinder changes slightly, resulting in a change in the optical path length of the fibers. If the piezoelectric cylinders are driven (180° out of phase) by a triangular voltage signal with a frequency of, for example, 8.3 kHz, the resulting changes in the fiber lengths modulate the optical path length difference between the two arms of the interferometer.
  • the interference pattern at the interferometer output will be modulated at 100 kHz, a frequency that is easily isolated by an electrical bandpass filter to increase the signal-to-noise ratio.
  • Alternative embodiments may employ a piezoelectric stack with a mirror attached thereto as a way of achieving high frequency length changes in a light path. That embodiment is described in more detail in Example 1 below.
  • Two different general methods can be used to scan a sample and create an OCM image.
  • a 2-D lateral scan at a fixed depth, then increment the depth, then perform another lateral scan, etc.
  • a 3-D image of a sample volume is then constructed by successively stacking 2-D optical sections that are parallel to the surface of the sample.
  • most researchers see, for example, Huang et al., 1991 a) perform a longitudinal (depth) scan at a fixed transverse point, then translate the beam laterally in a single direction and repeat the longitudinal scan, etc.
  • a 2-D optical section is then formed which is perpendicular to the sample surface, having one depth dimension and one lateral dimension.
  • Each longitudinal scan is accomplished by translating the reference mirror at speeds as high as 160 mm/s (Hee et al., 1994).
  • the light reflected from the moving reference mirror is then Doppler shifted by as much as 380 kHz, and the electrical bandpass filter can be set at that frequency.
  • the electrical bandpass filter can be set at that frequency.
  • this Doppler-shift technique it is difficult to keep the beam waist coincident with the coherence volume, resulting in degraded lateral resolution.
  • the lateral resolution of an OCM image is determined by the size of the focused beam. Thus, for good resolution, it is beneficial to use a focused spot less than 10 ⁇ m in diameter.
  • a selected focusing arrangement can be tested by imaging a Ronchi ruling through 1.2 mm of a highly scattering solution of polystyrene latex spheres.
  • the Ronchi ruling consists of 10 ⁇ m wide stripes of chrome deposited on a glass cover slip. The chrome stripes are separated by 10 ⁇ m stripes of clear glass.
  • the highly scattering solution serves as a tissue phantom and consists of 0.523 ⁇ m diameter polystyrene latex spheres.
  • the sphere solution represents nearly 5 optical depths and appears opaque to the unaided eye or through a conventional microscope. From a detailed analysis of images like FIG. 2, the l/e 2 diameter of the beam waist was determined to be 8.8 ⁇ 0.2 ⁇ m, just slightly larger than the diffraction-limited spot size of 8 ⁇ m.
  • a critical factor is the time needed to acquire an image. Certainly this time should be short compared to the mean time between cell divisions, and it would be helpful if the acquisition time were short enough to eliminate gross motion of the embryo.
  • the fundamental physical phenomenon that places a minimum on the acquisition time is photon noise. For example, to obtain 3% precision in the collected signal at each voxel in a 3-D image of an embryo, assuming Poisson statistics, there must be about 10 3 photons in the collected signal for an average voxel.
  • the collected signal is proportional to the amplitude of the interference fringes at the output of the interferometer.
  • the interference term is proportional to the electric field back-scattered from a voxel, so the collected signal is proportional to the square-root of the back-scattered power (Izatt et al., 1994a). If P o is the power incident upon the interferometer, and P(z) is the power returning from a voxel at depth z, then:
  • ⁇ back is the back-scattering coefficient (1/m)
  • l coh is the coherence length of the source.
  • Equation (2) P o exp( ⁇ t z) is the power reaching a depth z in the sample without being scattered or absorbed, ⁇ back l coh /2 is the fraction of that power that is back-scattered and can coherently interfere at the output of the interferometer, and exp( ⁇ t z) is the fraction of the back-scattered light that reaches the surface of the medium without being scattered or absorbed.
  • OCM data can be used in conjunction with equations (1) and (2) to deduce values for ⁇ t and ⁇ back in tissue.
  • Clivaz et al. (1992) have used OCM to measure the scattering properties, refractive index, and thickness of arterial walls.
  • Schmitt et al. (1994a) used Monte Carlo simulations to show that the single-scattering model of equation (2) is valid in a medium up to 4 or 5 optical depths (4 or 5 / ⁇ t ).
  • Schmitt et al. (1993) measured ⁇ t to be about 5/mm (and ⁇ back to be about 1.5/mm) in the dermis of the human finger and forearm. At greater than 4 to 5 optical depths, multiple scattering begins to become important, and resolution may be degraded.
  • Izatt et al. (1994a) show that OCM has its greatest advantage over confocal microscopy between 5 and 15 optical depths.
  • Schmitt et al. (1994c) studied the walls of freshly excised rat coronary arteries with OCM. Using focused beam spots with diameters ranging from 8 to 17 ⁇ m, they measured higher total attenuation coefficients with larger beam spots. They concluded that the increase in measured ⁇ t was a result of degradation of spatial coherence across the beam with increasing beam diameter. They speculated that this degradation was due to spatial fluctuations in the refractive index in the artery walls, and suggested a theoretical framework based on the mutual coherence function of the beam that might begin to describe quantitatively the observed loss in spatial coherence.
  • OCM optical cosine-derived mammal endometrial senor
  • One important calibration procedure is to use the OCM to examine tissue phantoms with carefully constructed optical properties and physical dimensions.
  • the solutions can be made of polystyrene latex spheres or Intralipid, a fat emulsion used for intravenous feeding in hospitals.
  • the spheres are available in precise diameters; Mie theory can be used to calculate the scattering coefficient of sphere solutions as well as the asymmetry parameter g , the mean cosine of the scattering angle.
  • Intralipid contains a wide continuum of particle sizes, but its optical properties have been studied exhaustively because it is less expensive than the latex spheres (Driver et al., 1989; Flock et al., 1987, 1992; van Staveren et al., 1991). Values for ⁇ t for solutions of spheres and Intralipid can be measured with a spectrophotometer using a successive dilution technique.
  • Lateral and depth resolution can be checked by placing a resolution target or a microscope calibration reticle at an interface between layers in a tissue phantom.
  • Slopes, intercepts, and discontinuities in data from a longitudinal scan can be used to deduce ⁇ t and ⁇ back for the various layers in a phantom (Schmitt et al., 1993).
  • Longitudinal scans of a solution of polystyrene spheres (used also in FIG. 2) showed that measured fringe visibility falls off exponentially with depth as predicted by equation (2), and a value for ⁇ t of 38.4 ⁇ 0.2 /cm.
  • a series of spectrophotometer measurements yielded ⁇ t of 40.0 ⁇ 0.1 /cm. The discrepancy is probably due to the small contribution of multiply-scattered photons.
  • Image acquisition may be directed by a computer system running visualization software such as, for example, LabView (from National Instruments).
  • LabView from National Instruments
  • an image may consist of 500,000 voxels and cover a volume of 1 mm ⁇ 1 mm ⁇ 1 mm.
  • the invention may be applied to images of any number of voxels, whether fewer than 500,000 voxels or more than many millions of voxels. Desired voxel number will be selected based on the volume to be imaged and the resolution desired.
  • Horizontal slices of images may be viewed during data acquisition, and after collection a 3-D image can be viewed quickly as a time series of horizontal slices displayed on a computer monitor.
  • More extensive examination of a 3-D image may be accomplished by transferring the image to a Unix workstation running an advanced software package such as, for example, AVS 5.0 (Advanced Visualization Systems).
  • a particularly useful way to extract information from an image is to rotate a volume rendering of the image, noting alignment of structural features.
  • a volume rendered image the contribution of a voxel at the rear of the image volume is “blended” with contributions from all voxels along the line projecting forward to the final pixel in the 2-D image.
  • FIG. 1 Several of the Figures included herewith are simply volume-rendered images viewed from a single perspective, then printed on a color laser printer. The information content of these laser printer images is significantly less than the rotating volume-rendered images on the computer monitor.
  • FIGS. 3 and 4 are typical plots of OCM fringe amplitude versus depth, averaged over horizontal slices in plant and frog preparations, respectively. Fringe amplitude is proportional to the square-root of power backscattered from the sample, so it should decay exponentially with depth according to exp( ⁇ total depth). Fitted values for ⁇ total are 15 and 10/mm for plant and frog tissue, corresponding to optical depths (l/e attenuation lengths) of 70 ⁇ m and 100 ⁇ m, respectively.
  • the modified OCM is faster than the original instrument because the x-y scans are performed by galvo-scanning mirrors instead of DC motor translators.
  • a piezo-mounted reference mirror produces output fringes at 125 kHz instead of the 2 kHz frequency achieved by wrapping optical fiber around a piezo-cylinder.
  • a lower response time for the electrical filters that selectively pass the first two harmonics of the fringe frequency can be achieved by widening the bandpass of these filters.
  • the rms integrated circuit that may be used to measure the amplitude of the fringe signal has an inherently low dynamic range.
  • Digital signal processing (DSP) is therefore a desirable alternative to analog circuits.
  • a DSP solution can permit modifications to the filter characteristics in software, with the response time to be determined by the integer number of fringe periods that are sampled. The dynamic range thus can be improved over the analog rms chip because multiplications are performed digitally.
  • photodetector noise at 100 kHz is 25 pW/sqrt(Hz), a factor of 8 greater than the manufacturer's specification (New Focus, Model 1801).
  • a similar silicon photodiode/amplifier hybrid from Advanced Photonix Model SD 100-41-21-23-1
  • the amplifier in the Advanced Photonix photodetector has a bandwidth of 400 kHz compared with 125 MHz for the New Focus detector.
  • the Advanced Photonix photodiode operates with a reverse bias of 15 Volts, while the New Focus diode has no bias. This reduction in photodetector noise reduced overall noise levels to the rage of fundamental photon noise.
  • FIG. 5 illustrates that the typical OCM interferometer output of 25 ⁇ W is accompanied by photon noise that is primarily Bose-Einstein. This ultimately means that the OCM achieves its maximum signal-to-noise ratio when the reference beam is cut to 3 ⁇ W.
  • Piezoelectric crystals are used in a variety of forms for phase modulation in interferometry.
  • the mirror in the reference arm of a Michelson interferometer is often attached to a piezo stack that is driven at frequencies up to 10 kHz, well below its resonance frequency. With driving amplitudes of some ten to a hundred volts, pathlength modulations of the order of a few ⁇ m can be achieved.
  • the fiber In fiber optic interferometers, the fiber can be wound in a large number of turns around a hollow piezoelectric cylinder. Driving the cylinder up to frequencies of a few kHz will cause it to expand and contract radially, stretching and relaxing the fiber accordingly and thus providing the modulation of the optical path length.
  • This Example describes the use of a piezoelectric stack that is driven at a resonance frequency of 125 kHz to produce a displacement amplitude of 400 nm with a peak-to-peak driving voltage of only 6.7 V.
  • Piezoelectric stacks manufactured by NEC Corporation of Japan were tested for possible use in the Michelson interferometer of the OCM of the invention.
  • Driving the piezos at their resonance frequency proved to be a method for circumventing these problems.
  • the electrical behavior of the unmounted piezo was tested by measuring its impedance as a function of frequency (see FIG. 6 ). At frequencies well below resonance, the piezo behaves like a capacitor, with the impedance inversely proportional to the frequency and the voltage lagging the current by approximately 90 degrees. At 255 kHz the unmounted piezo experiences a minimum in impedance, and voltage and current are in phase. This frequency is commonly referred to as the electrical resonance frequency of the piezo. At 330 kHz a maximum in impedance occurs, and again voltage and current are in phase—the electrical antiresonance frequency of the piezo. Between resonance and antiresonance the impedance increases with frequency, while the voltage leads the current by about 90 degrees. At frequencies higher than the antiresonance, the piezo again shows a capacitor-like behavior.
  • a small, lightweight mirror (1.5 mm ⁇ 1.5 mm ⁇ 0.1 mm, from Edmund Scientific Co., Barrington, N.J.) was attached to its face with cyanoacrylate (“super glue”).
  • the piezo stack with the attached mirror was either glued directly onto a standard adjustable mirror mount or glued onto a 25 mm diameter aluminum disk of 5 mm thickness, which was then held by a mirror mount.
  • gluing the lightweight mirror to the piezo did not alter its electrical behavior, attaching the stack to the aluminum disk or the mirror mount significantly changed the piezo's electrical resonance characteristics. Instead of the single electrical anti-resonance of the unmounted piezo, several anti-resonances at frequencies both lower and higher than the original one appeared.
  • FIG. 6 also shows the impedance of the mounted piezo as a function of the driving voltage frequency.
  • This piezo had been glued to an aluminum disk with an epoxy intended for fiber optic connectors (F 120, from Thorlabs Inc., Newton, N.J.).
  • the mechanical behavior of the piezo-mirror was tested in one arm of a Michelson interferometer with a helium-neon laser (633 nm) as a light source.
  • the frequencies of maximum piezo displacement are those of maximum impedance.
  • the mechanical resonance of the piezo is thus coincident with its electrical anti-resonance.
  • those frequencies are referred to as resonances for which the piezo experiences a maximum in displacement.
  • FIG. 7 shows the displacement of the piezo per volt applied at each of the resonance frequencies. For a particular resonance frequency, the piezo displacement was observed to increase linearly with increasing driving voltage amplitude.
  • the displacement per volt varies for the different resonances of the same piezo and decreases at higher frequencies.
  • the displacement per volt is higher at the 56 kHz resonance by almost a factor of three, the piezo in the Michelson interferometer was instead driven at the 125 kHz resonance because of its higher frequency (see Section 5).
  • the piezo mounted with super glue expands primarily in the free direction, its center of mass translates, in contrast with the piezo in epoxy, which may expand and contract about its center of mass.
  • the piezo mounted with super glue then has a greater effective mass as it resonates, yielding lower resonance frequencies.
  • the disk on which the piezo is mounted can play an important role in determining the positions of the resonance frequencies.
  • the described NEC piezo with superglue-mounted mirror, epoxy-mounted onto a 5 mm thick aluminum disk provides a displacement of around 400 nm at a resonance frequency of about 125 kHz, making it ideally suited for phase modulation in the OCM of the invention.
  • the superluminescent diode (SLD) light source in the tested OCM has a wavelength of 850 nm. Therefore, a piezo displacement of 400 nm produces a total pathlength difference between sample and reference arms in the OCM of less than one wavelength ( ⁇ ), i.e., modulation is over less than one fringe. For such small pathlength modulations, the interferometer output fringe signal will take on distinctly different shapes depending on the initial phase relation between the sample an d reference beams.
  • FIG. 8 illustrates this point for a modulation of one-half fringe (piezo displacement of 0.25 ⁇ ).
  • Graph (a) in FIG. 8 shows the piezo displacement which is simply of the form d o sin ⁇ t, where the peak-to-peak displacement 2-D o is taken to be 0.25 ⁇ .
  • the interference term in the corresponding interferometer output intensity is given by:
  • I out I o cos( ⁇ sin ⁇ t+ ⁇ )
  • the power P 1 , in the fundamental frequency ⁇ and the power P 2 in the second harmonic 2 ⁇ can be expressed as:
  • the sum P 1 +P 2 is independent of drifts in the pathlength difference between the two arms and is therefore a useful measure of the AC-coupled interferometer output fringe intensity.
  • FIG. 9 shows the experimental values for the powers of the interferometer output signal in the first two harmonics as a function of the piezo driving voltage.
  • the powers at 122 kHz and at 244 kHz were observed with a spectrum analyzer as they varied with the drifting phase, and their maximum values were plotted.
  • a high fringe frequency has been achieved by driving a piezo at this same frequency and using a piezo resonance to obtain a modulation amplitude of roughly one fringe. It is also possible to achieve high fringe frequencies by driving a piezo at low frequencies but with large displacement amplitudes.
  • Cruz et al. reached fringe frequencies of 1 GHz with a peak-to-peak pathlength difference of 14 mm. In this case, phase drift ceases to be a problem because of the long train of fringes before the phase break associated with piezo reversal.
  • the large interferometer path differences inherent in this approach are incompatible with the operation of the OCM of the invention.
  • the OCM of the invention collects three-dimensional images by performing a series of fast two-dimensional scans in planes normal to the incident beam and at regular depth intervals in the sample. These two-dimensional “en face” scans are performed at depths determined by the interferometer's equal path length position in the sample. Because the typical depth interval for the OCM is about 5 ⁇ m, modulation in the path length difference must be limited to about 1 ⁇ m during one of the en face scans. Larger modulations would degrade the depth resolution of the OCM. Hence a piezo stack driven at its resonance frequency has provided both a high fringe frequency for fast OCM image acquisition and a small modulation amplitude for good depth resolution.
  • a piezoelectric stack when glued to an aluminum disk, displays a number of mechanical resonances between 50 and 350 kHz.
  • the piezo is driven at its 125 kHz resonance for fast phase modulation in a Michelson interferometer.
  • a piezo displacement of about 360 nm (0.42 ⁇ ) is achieved.
  • the long-term performance of the piezo under these conditions is reliable; in particular, no heating or other damage to the stack has been observed.
  • the measured rms value of the AC-coupled interferometer output experiences large variations due to phase wander between the reference and sample arms of the interferometer.
  • the sum of the powers of the first two harmonics of the driving frequency provides a measure of the interferometer output that is independent of phase drifts.
  • a modified OCM was constructed that is capable of collecting a million-voxel image in less than a minute.
  • An optical schematic of the instrument appears as FIG. 10.
  • the key changes in design from the original OCM involve the introduction of galvo-scanning mirrors for the x-y scans and the use of a piezo-mounted mirror for the production of interferometer fringes.
  • a pair of orthogonal galvoscanners deflects the collimated beam emerging from the sample fiber and varies its angle of incidence upon the focusing lens, thereby scanning the focused waist of the beam across the x-y plane in the sample.
  • the galvoscanners can be operated at up to 1 kHz.
  • the beam spends about 20 microseconds on a voxel, so a linear scan along the x-axis of 100 voxels takes 2 milliseconds.
  • the fast x-axis galvo is operated at slightly less than 500 Hz.
  • a million-voxel image could therefore be taken in 20 seconds, though overhead in processing each x-y scan and moving the DC motor actuators along the z-axis increases the collection time to 40 to 60 seconds.
  • the galvoscanners were calibrated by imaging a Ronchi ruling with a period of 20 ⁇ m.
  • the brightness of a voxel in an OCM image is proportional to the amplitude of the OCM interferometer fringes. At each voxel, the amplitude of the fringes must be determined.
  • the modified OCM spends just 20 microseconds on a voxel, so the frequency of the fringes must be at least 50 kHz.
  • a small reference mirror 1.5 mm ⁇ 1.5 mm ⁇ 0.1 mm, Edmund Scientific Co.
  • AE0203-DO4, Thorlabs was glued to a piezoelectric stack with a resonant frequency of 250 kHz.
  • the mirror/piezoelectric stack forms the rear end of the retroreflector in the reference arm of the OCM interferometer.
  • the path length difference in the interferometer varies and 120 kHz fringes appear at the output.
  • the fringes are isolated with a narrow bandwidth electrical filter, and the output is then sent to an rms circuit.
  • a commercially available integrated circuit is the AD63 7 (Analog Devices) that measures the amplitude of the fringes to better than 10% in approximately two periods of the fringe signal. Two periods at 120 kHz amount to 17 microseconds, so the beam spends 20 microseconds on each voxel.
  • the path length difference between the sample and reference arms of the OCM drifts slowly by roughly a half-wavelength (one fringe) due to air currents, temperature effects, etc.
  • This phase drift causes the fringe signal to shift power from the fundamental piezoelectric driving frequency (120 kHz) to higher harmonics and to a DC offset.
  • the output of the rms circuit may vary by 30 to 50% even when the scattering power of the voxel remains constant.
  • This problem is solved by constructing the electrical filter to pass the fundamental and first harmonic frequencies.
  • the design of the modified OCM has another notable advantage over that of the original OCM.
  • the original OCM about 10 m of optical fiber was wrapped under tension around a piezoelectric cylinder.
  • a driving voltage was applied to the cylinder, stretching and contracting the fiber, and causing the optical path length of the fiber to oscillate.
  • a fiber/cylinder system was inserted into each of the sample and reference arms of the OCM interferometer. These two piezoelectric cylinders were driven 180° out of phase to produce fringes at the output of the OCM interferometer.
  • the stretching of these long lengths of fiber led to noticeable stress birefringence, and “paddles” were incorporated to twist the fiber systematically until the optical path lengths for the two polarization states of the beam were equal.
  • the setting of the paddles was subject to drift, leading to distorted visibility curves of the interferometer fringes.
  • the lengths of the optical fiber in the sample and reference arms are just 1 meter. No stretching of the fiber occurs, and no distortion of the Gaussian visibility curve over time has been noted.
  • Three-dimensional OCM images can be generated by adapting available visualization software, such as, for example, AVS (Advanced Visual Systems) Version 5.0 to display 3-D OCM images on Unix workstations.
  • AVS Advanced Visual Systems
  • VISUALIZATION EXPRESS also by AVS does not require a Unix workstation.
  • VISUALIZATION EXPRESS is written in OpenGL, which allows graphics applications to be ported to many software/hardware platforms. This software was adapted to create a custom graphical user interface called “Intuitive Network” within Visualization Express and achieved increased flexibility and power. The following is a brief description of the fundamental principles of this image-display software package.
  • the OCM assigns a single number to each of the roughly one million voxels scanned in the sample volume. To first approximation, this number is a measure of the light scattering power of the associated voxel. To visualize one of these 3-D data volumes, all voxels must be projected onto a 2-D computer screen for viewing. The process of projecting voxels, including assigning the relative weights of voxels deep within the volume versus near the surface of the volume, is called volume rendering.
  • volume rendering is ray tracing. Every pixel in the 2-D image to be generated on the computer screen determines a ray that is drawn from the pixel on the 2-D screen through the 3-D data volume. A “parallel projection” is employed, in which projected rays are parallel to each other. All voxels in the volume along a ray contribute to the value of the corresponding pixel on the 2-D computer screen. Because a ray does not always go through the centers of voxels that it intersects, there are different ways to compute (or “blend”) the contributions of voxels along the ray.
  • opacity factor Another feature involved in the blending of voxels along a ray is the “opacity” factor.
  • the content of each voxel is multiplied by the opacity factor as the sum is formed along a given ray. If the opacity factor for all voxels is zero, no voxel contributes to a pixel, and the pixel is black. If the opacity factor for all voxels is one, the voxel contents are summed along the ray and the resulting pixel may contain a large number, perhaps a number representing saturation. Small values for the opacity factor tend to avoid saturation and allow voxels deep in the image volume to contribute meaningfully to the corresponding pixel. That is, small values of the opacity factor tend to impart a more “transparent” appearance to the image volume.
  • the OCM of the invention assigns a raw number (grey level) to a voxel based upon its measured light scattering power.
  • AVS VISUALIZATION EXPRESS uses false color to help distinguish different grey levels in the raw voxel contents.
  • Two different ways were used for implementing false color in the volume-rendering algorithms available in AVS Express.
  • the simpler way, named “SFP”, is to apply the ray-tracing algorithm for volume rendering (described above) to the raw greyscale contents of voxels.
  • the resulting 2-D greyscale pixels are then color coded, e.g., weak pixels are assigned the color blue and strong pixels are colored red.
  • a particular region of the 3-D volume may change color drastically as the volume is viewed from different vantage points. For example, two green voxels can be superposed along a particular line of sight to yield a red pixel.
  • volume-rendering method named “DC”
  • the raw contents of voxels are color coded, i.e., values for red, green, and blue are assigned to each voxel based upon the voxel's raw grey level.
  • the ray tracing algorithm for volume rendering is executed separately for all three colors to generate a colored 2-D image on the computer screen.
  • This DC method does indeed superpose two green voxels to yield a strong green pixel. In this way, a region of the image volume with a particular light-scattering strength will retain its color, at least approximately, as the volume is rotated on the screen.
  • the software allows anatomical, morphological and histological aspects of plants, frogs, and other organisms to be examined. Examples of AVS software settings are as follows:
  • the OCM was also used to study the temporal changes in the shoot apical meristem and shoot apex during successive leaf initiations. For these observations, the plants were grown in four-inch pots in soil under an 8-hour day length to inhibit the transition from vegetative to reproductive development. These growth conditions permitted observation of meristem activity over many consecutive leaf initiation events. As humidity variations appeared to have significant effects on plant growth rates, it is preferable to maintain the plants in a humidity-controlled growth chamber. In addition to allowing precise regulation of the environment in which the plants grow, such a chamber allows growth of populations of plants under long-day conditions (for studies on embryo formation) and short day conditions (for studies on phyllotaxy) at the same time.
  • a rotated image of the leaf and meristem region was visualized, having a volume of (200 ⁇ m ⁇ 200 ⁇ m ⁇ 120 ⁇ m) (width ⁇ width ⁇ depth) with a voxel size of (2 ⁇ m) 3 .
  • the leaves were seen growing out from the center of the shoot.
  • the meristem and shoot apex were evident at the base of the leaves.
  • the “opacity” parameter (see Example III on the image-rendering software) was adjusted so that opacity was high. With this setting, weakly scattering tissues (blue) surrounding strongly scattering tissues (red/yellow) hid the strongly scattering regions from view. The overall effect was that the “outside” of the plant was visible, as in a scanning electron micrograph. By cropping or slicing into the image plane of the strongly scattering tissue, the red/yellow was exposed.
  • the opacity parameter was adjusted low so that voxels deep in the tissue could be seen.
  • Identifying the smaller leaf primordia was more difficult.
  • To unambiguously identify the smaller organs frequent observations were made, e.g., every hour or two, to observe their increase in size during development. All images were acquired with the original OCM which requires 3 hours for a million-voxel image. Therefore a single image averages over significant growth, and this averaging is probably a factor in the resolution of the image.
  • the modified OCM has an image acquisition time of 5 minutes or less for similar images. Use of the modified OCM produced a series of images more closely spaced in time, and allowed identification of leaf primordia as they emerged from the meristem.
  • the OCM image included leaves and a small, strongly scattering region that was consistent with a leaf primordium.
  • the histological section of a comparable plant supported this interpretation.
  • the OCM image was cropped from the top and was an “outside” image (high opacity), so that the meristem below was not visible.
  • the shootmeristemless mutant is known to lack a shoot apical meristem (Barton and Poethig, 1993).
  • the apical meristem appeared as a red, highly light scattering structure.
  • the shootmeristemless mutant there was no such structure. Instead a gap indicating a lack of a shoot apical meristem was detected.
  • the OCM can be used, not only to visualize structures in a biological sample, but also to visualize developmental stages, processes, and events, to contrast mutants with non-mutants or to grade mutant or allelic series, and the like.
  • the effect of a variety of factors on light scattering can also be used to characterize biological samples with respect to such factors, including, for example, gene activity, differentiation, cell elongation, cell dormancy, stress response, pathogen response, and the like.
  • Uses of light scattering comparisons employing the OCM of the invention will be evident to those engaged in such comparisons, for correlating light scattering or other OCM image characteristics with a variety of conditions, structures, and events of interest.
  • A. Xenopus embryos are mounted in a small, triangular well cut in a layer in the bottom of a petri dish coated with silicone rubber.
  • a 100 ⁇ m thick sheet of gelled agarose is placed over the top of the embryo and secured in place with thin cactus spines stuck into the silicone rubber.
  • This method of stabilizing the embryo keeps the embryo in a defined position and orientation, without the danger of distorting the cell movements under study.
  • gastrulation a set of three-dimensional images through the thickness of the animal pole of the embryo is collected. These three-dimensional data sets are processed and rendered into a time-lapse movie. As the resolution of the OCM is smaller than the single cells, these images are adequate to follow the tissue movements of gastrulation.
  • two-dimensional images may be collected, in the plane bisecting the embryo along its midline. This offers rapid frame rates, and therefore better details on the cell movements within this reduced field of view.
  • the OCM system is used to examine the morphological patterning of the mesoderm after it involutes. This process is critical for the resulting structures, such as the notochord and the somites, as well as for the nervous system. Interactions between the notochord and the spinal cord affect the dorsoventral patterning of the nervous system, and interactions with the somites result in segmentation of the sensory nervous system and the ventral roots of the motoneuron axons formed by the spinal cord.
  • the experimental arrangement described above is used to stabilize the embryos, and the OCM is employed to collect images needed for 2- and 3-dimensional time-lapse movies.
  • the volume imaged was (600 ⁇ m ⁇ 600 ⁇ m ⁇ 420 ⁇ m) (width ⁇ width ⁇ depth), and the voxel size was (6 ⁇ m) 3 .
  • the beam was still incident upon the embryo's left side from the top of the image.
  • the view was again along the body axis, but looking toward the tail, so the dorsal side was on the left and the ventral side was on the right.
  • the 600 ⁇ m long segment that was imaged was further down the body from the head.
  • the 420 ⁇ m depth was oriented top-bottom in the figure, and the 600 ⁇ m dorsal-ventral width lay left-right.
  • the 3-D image was been carefully rotated so that the view was straight down the axis of the spinal cord a rotation of just one degree about the beam axis (top-bottom axis) would obscure the structure that was obvious at the selected viewing angle.

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